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Name: Julie
Status: educator
Grade: other
Location: AL
Country: N/A
Date: 4/7/2005


Question:
Does the density of different balls effect the distance that they travel?


Replies:
Julie,

If the only force affecting the ball is gravity, density does not matter. Mass and size also have no effect. However, density does affect the motion when a ball travels in air (or any other gas).

Air pressure depends on speed and size (specifically the cross-sectional area). For a ball, this is of course pi times the radius-squared. The force of air resistance does not depend on the ball's mass. The contribution to a balls acceleration due to air resistance (F/m) is proportional to the ratio r^2/m. Density is proportional to m/r^3. If radii are similar, the ball with the greater density is affected less by air resistance. A bowling ball is larger than a tennis ball, but air resistance affects a bowling ball's motion much less than it affects a tennis ball.

Ken Mellendorf
Math, Science, Engineering
Illinois Central College


Sure, Julie, due to air drag. In a vacuum it would not matter, but in our atmosphere it matters a fair amount to fast-moving balls. As ball move slower and slower it will matter less and less.

Plastic wiffle-balls are the same size as base-balls, but they have less density and less mass. They travel much less distance when hit hard.

To keep the same mass while varying the density, you might find a big wiffle-ball with the same weight as a little golf-ball. The higher-density ball will travel farther in that case, too, given the same speed.

There is an idea called "ballistic coefficient". ballistic_coefficient = ( mass / frontal_area ). Things with the same ballistic coefficient tend to travel about the same distance through the air. Things with higher ballistic coefficients tend to travel greater distances. An arrow made of wood needs to be longer than an arrow made of iron, to have the same ballistic coefficient.

This never exactly matches the idea of density.

density = ( mass / volume ).

You can reconcile them a little bit by understanding:

volume = ( frontal_area x length ) (approximately)
ballistic_coefficient = ( density * length )

So a big soft-ball will travel farther than a little baseball of the same density.

Jim Swenson


Short answer, Yes.

Long answer, only in an atmosphere. The greater the density of a ball, the more mass it has at a given size. (Boulders are far more massive than beach balls!) Whenever anything moves through the air, there is resistance roughly proportional to its surface area. This resistance acts as a force to slow that object down. The more massive the object, the more force required to slow it.

So if you took the aforementioned beach ball, and a boulder of the same size, and chucked them both with a catapult...

-The beach ball would quickly slow to a near stop in the air, and drop to the ground.

-The Boulder would go sailing through the air with only a trivial drop in its forward momentum.

All of this is of course assuming both objects are the same shape, and can be launched at the same velocity.

Ryan Belscamper



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